2.3.26 Problems 2501 to 2600

Table 2.625: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2501	2254	\begin{align*} y_{1}^{\prime }&=-y_{2} \\ y_{2}^{\prime }&=y_{1}-2 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.326
2502	3937	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=36 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.326
2503	6569	\begin{align*} \sqrt {y}\, y^{\prime \prime }&=2 b x +2 a \\ \end{align*}	✗	✓	✗	✗	0.326
2504	6693	\begin{align*} -y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
2505	10531	\begin{align*} \left (x +4\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.326
2506	11060	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.326
2507	11072	\begin{align*} y^{\prime \prime }-\frac {2 \left (1+t \right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1}&=0 \\ \end{align*}	✓	✓	✓	✗	0.326
2508	11167	\begin{align*} y^{\prime \prime }+q y^{\prime }&=\frac {2 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	0.326
2509	12811	\begin{align*} 12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
2510	13090	\begin{align*} x^{\prime \prime }&=a x+b y \\ y^{\prime \prime }&=c x+d y \\ \end{align*}	✗	✓	✓	✓	0.326
2511	13126	\begin{align*} x&=t x^{\prime }+f \left (x^{\prime }, y^{\prime }\right ) \\ y&=y^{\prime } t +g \left (x^{\prime }, y^{\prime }\right ) \\ \end{align*}	✗	✓	✓	✓	0.326
2512	14568	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.326
2513	14951	\begin{align*} t^{2} y^{\prime \prime }-\left (t^{2}+2 t \right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.326
2514	17823	\begin{align*} x^{\prime }&=0 \\ y^{\prime }&=-2 y \\ \end{align*}	✓	✓	✓	✓	0.326
2515	18101	\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
2516	3062	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.327
2517	13116	\begin{align*} x^{\prime }&=\left (a y+b \right ) x \\ y^{\prime }&=\left (c x+d \right ) y \\ \end{align*}	✗	✓	✓	✗	0.327
2518	17661	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 y^{\prime } x&=-8 \\ \end{align*}	✓	✓	✓	✓	0.327
2519	10746	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.328
2520	22646	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.328
2521	380	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.329
2522	518	\begin{align*} 36 x^{2} y^{\prime \prime }+60 y^{\prime } x +\left (9 x^{3}-5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
2523	2235	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=F \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.329
2524	4117	\begin{align*} y^{\prime \prime }+8 y^{\prime }+15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
2525	8857	\begin{align*} y^{\prime \prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.329
2526	11052	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.329
2527	11074	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.329
2528	14126	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=x^{2}-x \\ \end{align*}	✓	✓	✓	✓	0.329
2529	14947	\begin{align*} x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x&={\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.329
2530	16966	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
2531	17226	\begin{align*} 2 t y^{2}+2 t^{2} y y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.329
2532	18622	\begin{align*} 5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
2533	23227	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
2534	23332	\begin{align*} y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
2535	23341	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
2536	26770	\begin{align*} x^{\prime }&=3 x-22 \sin \left (y\right )+x^{2}-y^{3} \\ y^{\prime }&=\sin \left (x\right )-5 y+{\mathrm e}^{x^{2}}-1 \\ \end{align*}	✗	✗	✗	✗	0.329
2537	273	\begin{align*} y^{\prime \prime }+y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.330
2538	1052	\begin{align*} y^{\prime \prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.330
2539	1280	\begin{align*} 9 y^{\prime \prime }+9 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.330
2540	3788	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.330
2541	6304	\begin{align*} y^{\prime \prime }&=a +y x +2 y^{3} \\ \end{align*}	✗	✗	✗	✗	0.330
2542	10623	\begin{align*} 9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.330
2543	10633	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.330
2544	6715	\begin{align*} -y+y^{\prime } x +4 x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
2545	8936	\begin{align*} y^{\prime \prime \prime \prime }+16 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.331
2546	10530	\begin{align*} \left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
2547	10814	\begin{align*} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
2548	11162	\begin{align*} y^{\prime \prime }-a^{2} y&=\frac {6 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.331
2549	11205	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
2550	13095	\begin{align*} x^{\prime \prime }-a y^{\prime }+b x&=0 \\ y^{\prime \prime }+a x^{\prime }+b y&=0 \\ \end{align*}	✗	✓	✓	✓	0.331
2551	15099	\begin{align*} x^{3} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
2552	26775	\begin{align*} x^{\prime }&=\frac {3 \sin \left (x\right )}{4}-7 y \left (1-y\right )^{{1}/{3}}+x^{3} \\ y^{\prime }&=\frac {2 x}{3}-3 y \cos \left (y\right )-11 y^{5} \\ \end{align*}	✗	✗	✗	✗	0.331
2553	523	\begin{align*} 2 x^{2} y^{\prime \prime }-3 y^{\prime } x -2 \left (-x^{5}+14\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
2554	1054	\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.332
2555	3267	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
2556	3922	\begin{align*} x_{1}^{\prime }&=-4 x_{1} \\ x_{2}^{\prime }&=-4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.332
2557	6617	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=-3 \,{\mathrm e}^{2 x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.332
2558	10565	\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
2559	10737	\begin{align*} y^{\prime \prime }-a^{2} y&=\frac {6 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.332
2560	10941	\begin{align*} \left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
2561	11071	\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.332
2562	18571	\begin{align*} 2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
2563	19857	\begin{align*} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.332
2564	26772	\begin{align*} x^{\prime }&=7 x+2 \sin \left (y\right )-4 y^{4} \\ y^{\prime }&={\mathrm e}^{x}-3 y-1+\frac {5 x^{2}}{2} \\ \end{align*}	✗	✗	✗	✗	0.332
2565	26777	\begin{align*} x^{\prime }&=5 x+y \cos \left (y\right )-\frac {x^{3}}{3} \\ y^{\prime }&=3 x+2 y+\frac {x^{4}}{12}-y^{3} {\mathrm e}^{y} \\ \end{align*}	✗	✗	✗	✗	0.332
2566	276	\begin{align*} y^{\prime \prime }+5 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.333
2567	10706	\begin{align*} x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.333
2568	11010	\begin{align*} 9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.333
2569	14998	\(\left [\begin {array}{cc} 3 & -1 \\ 1 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.333
2570	17416	\begin{align*} y^{\prime \prime }+6 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.333
2571	18754	\begin{align*} y^{\prime \prime } x -\left (x +n \right ) y^{\prime }+n y&=0 \\ \end{align*}	✓	✓	✓	✗	0.333
2572	20139	\begin{align*} y^{\left (5\right )}-m^{2} y^{\prime \prime \prime }&={\mathrm e}^{a x} \\ \end{align*}	✓	✓	✓	✓	0.333
2573	7142	\begin{align*} x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (1+y\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.334
2574	10981	\begin{align*} x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.334
2575	12785	\begin{align*} y^{\prime \prime \prime \prime }-12 y^{\prime \prime }+12 y-16 x^{4} {\mathrm e}^{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.334
2576	13117	\begin{align*} x^{\prime }&=x \left (a \left (p x+q y\right )+\alpha \right ) \\ y^{\prime }&=y \left (\beta +b \left (p x+q y\right )\right ) \\ \end{align*}	✗	✗	✗	✗	0.334
2577	278	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.335
2578	440	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.335
2579	2413	\begin{align*} y^{\prime \prime }-t y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.335
2580	6699	\begin{align*} 2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.335
2581	6738	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=4+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.335
2582	9103	\begin{align*} y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.335
2583	10780	\begin{align*} 2 y^{\prime \prime } x -\left (2 x +3\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.335
2584	17017	\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.335
2585	17733	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.335
2586	243	\begin{align*} 35 y^{\prime \prime }-y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
2587	355	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=x +1 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.336
2588	439	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.336
2589	2256	\begin{align*} y_{1}^{\prime }&=3 y_{1}+y_{2} \\ y_{2}^{\prime }&=-y_{1}+y_{2} \\ \end{align*}	✓	✓	✓	✓	0.336
2590	2316	\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\cos \left (t \right ) \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.336
2591	2365	\begin{align*} y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
2592	3695	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
2593	7989	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&=5 \\ \end{align*}	✓	✓	✓	✓	0.336
2594	10992	\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.336
2595	13088	\begin{align*} t x^{\prime }-y^{\prime } t -2 y&=0 \\ t x^{\prime \prime }+2 x^{\prime }+t x&=0 \\ \end{align*}	✗	✓	✓	✗	0.336
2596	17384	\begin{align*} y^{\prime \prime }+5 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
2597	20106	\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
2598	21199	\begin{align*} x^{\prime \prime \prime }-x^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.336
2599	23305	\begin{align*} y^{\prime \prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
2600	27198	\begin{align*} x^{\prime }&=x-\frac {x y}{2} \\ y^{\prime }&=2 x y-\frac {6 y}{5} \\ \end{align*}	✗	✓	✓	✗	0.336